基于小波基的乘积加权 Besov 空间和乘积加权 Triebel-Lizorkin 空间的 Plancherel-Pôlya 型刻画

数学物理学报 ›› 2025, Vol. 45 ›› Issue (3): 665-686.

基于小波基的乘积加权 Besov 空间和乘积加权 Triebel-Lizorkin 空间的 Plancherel-Pôlya 型刻画

李子燕(),陶祥兴^*()

浙江科技大学理学院杭州 310023

收稿日期:2024-05-20 修回日期:2025-01-26 出版日期:2025-06-26 发布日期:2025-06-20
通讯作者: *陶祥兴, E-mail: xxtao@zust.edu.cn
作者简介:李子燕, E-mail: liziyan0918@163.com
基金资助:
国家自然科学基金(12271483);浙江科技大学研究生科研创新基金(2023yjskc23)

Plancherel-Pôlya Type Characterization of Product Weighted Besov and Product Weighted Triebel-Lizorkin Spaces Based on Wavelet Basis

Li Ziyan(),Tao Xiangxing^*()

School of Science, Zhejiang University of Science and Technology, Hangzhou 310023

Received:2024-05-20 Revised:2025-01-26 Online:2025-06-26 Published:2025-06-20
Supported by:
NSFC(12271483);Postgraduate Research Innovation Fund of Zhejiang University of Science and Technology(2023yjskc23)

摘要/Abstract

摘要：

在 Coifman 与 Weiss 意义下的乘积齐型空间上, 该文利用小波基引入乘积加权 Besov 空间和乘积加权 Triebel-Lizorkin 空间, 通过乘积 Calderón 再生公式和几乎正交估计建立乘积加权 Besov 空间和乘积加权 Triebel-Lizorkin 空间的 Plancherel-Pôlya 型等价刻画, 函数空间及其范数独立于正交小波基的选取.

关键词: 加权 Besov 空间, 加权 Triebel-lizorkin 空间, 齐型空间, Plancherel-P?lya 型刻画

Abstract:

On the product spaces of homogeneous type in the sense of Coifman and Weiss, this paper introduces the product weighted Besov space and product weighted Triebel-Lizorkin space based on wavelet basis, and establishes the Plancherel-Pôlya type characterizations of product weighted Besov spaces and product Triebel-Lizorkin spaces via the wavelet reproducing formula and the almost orthogonal estimation, which means that the space are independent of the choice of the orthonormal wavelet basis.

Key words: weighted Besov space, weighted Triebel-Lizorkin space, spaces of homogeneous type, Plancherel-P?lya type characterization

中图分类号:

O174.3

李子燕, 陶祥兴. 基于小波基的乘积加权 Besov 空间和乘积加权 Triebel-Lizorkin 空间的 Plancherel-Pôlya 型刻画[J]. 数学物理学报, 2025, 45(3): 665-686.

Li Ziyan, Tao Xiangxing. Plancherel-Pôlya Type Characterization of Product Weighted Besov and Product Weighted Triebel-Lizorkin Spaces Based on Wavelet Basis[J]. Acta mathematica scientia,Series A, 2025, 45(3): 665-686.

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